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The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups

  • Book
  • © 2013

Overview

Authors:
  1. Daciberg Lima Goncalves

    1. Departamento de Matemática - IME, Universidade de São Paulo, São Paulo, Brazil

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  2. John Guaschi

    1. Laboratoire de Mathématiques Nicolas Oresme, Normandie Université UNICAEN, Caen Cedex, France

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction and Statement of the Main Results

    • Daciberg Lima Gonçalves, John Guaschi
    Pages 1-14

  3. Virtually Cyclic Groups: Generalities, Reduction and the Mapping Class Group

    • Daciberg Lima Gonçalves, John Guaschi
    Pages 15-50

  4. Realisation of the Elements of \(\mathbb V _{1}(n)\) and \(\mathbb V _{2}(n)\) in \(B_{n}(\mathbb{S }^{2})\)

    • Daciberg Lima Gonçalves, John Guaschi
    Pages 51-98

  5. Back Matter

    Pages 99-102
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Keywords

About this book

This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks an important step in the computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysis of their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups. This manuscript will serve as a reference for the study of braid groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra. ​

Authors and Affiliations

  • Departamento de Matemática - IME, Universidade de São Paulo, São Paulo, Brazil

    Daciberg Lima Goncalves

  • Laboratoire de Mathématiques Nicolas Oresme, Normandie Université UNICAEN, Caen Cedex, France

    John Guaschi

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